Note 50 — Chapter XIV · RELATIVISTIC MECHANICS

The identification of mass with energy necessitated by the Einstein theory allows us to obviate the paradoxical appearance of the following example: Consider an incandescent sphere radiating light in every direction. If placed at rest in some Galilean frame, it should remain there undisturbed, since the backward pressure exerted by the light radiation is distributed symmetrically round the sphere. But suppose now we view the incandescent sphere from some other Galilean frame moving away from the first with a velocity . From this new frame the incandescent sphere will be moving with a velocity , whereas the light waves radiated by it will still possess a velocity in all directions in our frame. It will then appear to us that the light waves are speeding away from the sphere in the direction of its motion with a velocity while they are traveling with a speed in the opposite direction. The conditions of light pressure will no longer be symmetrical, and calculation shows that the motion of the sphere should gradually slow down under the action of this resistance. Now this is impossible; for if the sphere appeared to us to be slowing down, it could never remain attached to its evenly moving Galilean frame, and we should be faced with a contradiction. As soon, however, as we recognise that the incandescent sphere by radiating light is losing energy and hence mass, the principle of the conservation of momentum shows that this gradual loss of mass would have for effect an increase in the velocity of the sphere and would thus compensate exactly the loss of velocity generated by the unsymmetrical light pressure. In this way the paradox is explained very simply.